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Fluent Math

- Multiplication

Multiply with Automaticity

An easy-to-use, automatic method to practice multiplication automaticity without stress.

Available for free on all devices!

(Schools may need a license.)
The flash card based Fluent Math app used in laptop, mobile and ipad to practice multiplication from memoryUse Fluent Math on any device (Chromebook, iOS, Android, tablets, computers, etc.)

From Strategies to Automaticity

Fluent Math is an innovative approach to practicing automaticity in the final stages of building fluency with basic multiplication facts. It allows each student the opportunity to automate as many facts as possible for them individually, before moving on to more advanced math.

For students who are fluent but not yet automatic, or for students in upper grades who don't know their facts well enough.

Help students move from conscious use of strategies to automaticity, without stress. Here's how:

Start practicing: It's very easy. Known facts are quickly verified.

Automatic pace: The entire table is reviewed in small rolling sets. Each student will progress at the right pace for them.

For facts not automated yet, students will have time to think and use their own strategies without time pressure. Each fact is then practiced a couple of times in succession until it can either be pulled from memory or answered efficiently. Spaced repetition with active retrieval helps in committing them to long-term memory. Learn, repeat, recall => automaticity.

Practice for 5 minutes, once or preferably twice a day.
Inspired by research.

Continue to read below on how to get started and why Fluent Math works so well...

Try it live right here

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Click the "Start practicing" button below.
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One of my students was so proud, she went from 14 to 72 correct multiplications in a 5-minute test after a week of app practice. She's so excited for tomorrow's test!

- Malin Wideheim, Special Education Teacher in Mathematics

We've been super happy! There are so many students who need easy access to practicing their times tables.

- Pernilla Olsson, Sixth Grade Teacher

What's been good is that you get to practice the same fact again if you were wrong. I've had time to think about the answer in my head.

- Student in Grade Seven

Start Using Fluent Math Now!

Fluent Math is a web app. Open multiplication.fluentmath.com on the device you want to use. Yeah, it's that easy!

Use asWeb App

Teachers, simply share the link with your class and let everyone practice individually for 5 minutes every morning and afternoon. You will see results in no time!

There is no login, as the results are stored in the browser, and there are no problems with privacy and GDPR, since no personal info is stored. Always use the same browser and device. Use 'Add to Home Screen' for an app-like experience.

Just open and practice. Fluent Math decides which facts to work on, as this enables auto-pacing and the use of smart repetition strategies.

Points are earned as progress is made over time, and once 1000 is reached, all facts have been provided efficiently!

Explore the Formative Assessment menu option to gain insights into the learning journey and identify challenges. It is a powerful tool for discovering the need for intervention and understanding the root cause of potential problems.

Fluent Math is also available as iOS app (with audio feedback when incorrect). Either with in-app purchase or as school edition for VPP.

Download on the App Store

Practice in a fun, stress-free, and efficient way

The Fluent Math app showing the home page and practice page

A Method in Line with the Times

Building fluency with basic multiplication facts starts in early elementary school with number sense, understanding, and strategy development. There are no shortcuts to fluency: it requires practice using a variety of methods, activities, games, and tools over a long time. Using cognitive effort is initially a good thing as brain bonds are developed and strategies are formed, challenged, and reformed. The more students think, the more they learn.

With repeated practice, students naturally become fluent at applying strategies and can do less thinking. They eventually move on to automaticity, which means answering without conscious thinking, as they either become very efficient at strategies or can pull facts from memory. This happens progressively and requires a lot of varied practice over time.

Automaticity in basic facts reduces cognitive load, freeing up resources for concepts like division, fractions, algebra, multi-step calculations, etc. The benefits affect almost all aspects of mathematics in later years.

Achieving automaticity from memory for all facts is difficult for many students. However, most can either become automatic with strategy or at least more efficient. Regardless, students should be allowed the opportunity to individually reach as far as possible towards automaticity, given its importance for future studies, according to research.

Practicing specifically for automaticity after having achieved fluency is not the same as rote memorization without understanding. Far from it. Trying to move facts to automaticity at this stage builds on students' own strategies and memory networks, which is a very different thing. It does not take away the importance of understanding and flexibility.

Students should only practice specifically for automaticity when they have a strong foundation of fluency:
• As preparation for upper grades, at the end of building fluency.
• When upper-grade teachers discover that their students are not automatic enough with their facts.
• As a yearly refresher and review of multiplication facts to improve retention and automaticity.

With a fast-paced curriculum, time is limited. While it is certainly possible to practice automaticity using manual methods, it can be challenging to manage individual practice with feedback and repetition of the right facts at the right time, especially for a whole class. Fortunately, this is a situation where digital tools excel.

Fluent Math is an automatic method to practice multiplication automaticity without stress. Teachers can, in an easy way, get the entire class to practice for 5 focused minutes every morning (and preferably afternoon). The entire multiplication table is reviewed, and each student practice individually at their own pace. Fluent Math automatically handles practice, repetition, spacing, and progress.

For kids, teenagers, and adults who need to review the multiplication tables, identify the facts they struggle with, and achieve automaticity.

How and Why It Works

Nerdy but interesting stuff...

How

Fluent Math is a fully automatic solution for practicing automaticity of the multiplication tables. Practice in 5-minute sessions with repetitive learning.

The entire table is reviewed, from 2x2 to 10x10 (or 12x12). Known multiplication facts are verified as quickly as possible. Facts that the student thinks about for too long or answers incorrectly are registered as "not automated" and then repeated with increased intervals, first after minutes, and then after hours and days. The repetition starts over if the student thinks for too long or answers incorrectly again. Eventually, the student will either become very fast at their strategy, or they will commit the fact to memory. This knowledge is then consolidated in long-term memory through spaced repetition with active recall.

For facts to be considered automated in this context, they must be answered correctly and quickly in at least three separate sessions each at least 4 hours apart.

This method results in individualization so the pace of learning is automatically adapted to each student (according to the principle of spaced repetition, Leitner system, Anki, etc.).

Why

Being able to multiply efficiently without conscious effort relieves the working memory aiding more advanced mathematics. It also improves confidence, which reduces the risk of math anxiety.

Students should not begin focusing on automaticity too soon, but first practice fluency for a long time using a variety of methods and tools.

When using the app, students can initially answer multiplication facts at their own pace and use their own strategies to calculate an answer without stress. Confidence is boosted as this means fewer mistakes (then under time pressure).

Repeated meaningful practice using the student's own strategies will enable the student to commit many basic multiplication facts to memory, reducing cognitive load, while practicing using these strategies flexibly and effectively in case the student forgets or cannot commit facts to memory.

The app is easy to use because it automatically determines what to practice and in what order.

Effective Learning

Once a student has proven the automation of the first commutative variant (e.g., 6 x 3 = 18), the second variant (3 x 6 = 18) is introduced in parallel, providing good opportunities for faster automation while strengthening the insight that the two are the same thing. This streamlines half the table.

The app also tries to take advantage of the learning technique 'interleaving' by including open statements (6 × _ = 18) when the student has begun to answer the multiplication quickly. This is to further challenge the student to note and reflect upon the relationship between the two commutative variants and the open statements (e.g., 6 × 3 =, 3 × 6 =, 6 × _ = 18, 3 × _ = 18, etc.), and to strengthen the memory association of them as a unit.

Since unused knowledge weakens, it is a good idea to review the tables annually. Consistent, long-term use of the app helps students of all ages with automaticity of the multiplication tables.

The solution has been inspired by research on active recall, spaced repetition, and interleaving.

Pricing

Web App: multiplication.fluentmath.com

Free

Free for private use.
Teachers can recommend it to students for use at home.
Schools may allow up to 10 students (e.g., those with special needs) per semester to use it free of charge in school.
Schools may test it in one class for two weeks for evaluation purposes.

A text like this is shown:

For private use only (Read more)

School License

Schools that allow more than 10 students per semester to access Fluent Math in school are required to pay an annual license fee of $160 (excluding VAT) per school.

Send an email to: support@fluentmath.com. The school will get a dedicated URL to use.

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Licensed to Pine Grove School

iOS App:

Free Edition - App Store

Free edition with in-app purchase.
For both private and in-school use.
Works identically to the web app, but also includes audio feedback* on facts when the answer is incorrect.
Free up to 7×7. Upgrade to premium (12×12) is available through in-app purchase.

School Edition - App Store

Paid edition, suitable for Apple School Manager and/or VPP.
For both private and in-school use.
Works identically to the web app, but also includes audio feedback* on facts when the answer is incorrect.
Premium edition, practice facts up to 12×12.

*Audio feedback is available in English or the following iOS languages when set: Spanish, Portuguese, French, German, Italian, Greek, Chinese, Hindi, Russian, Japanese, Arabic, Bengali, Swedish, Danish, Norwegian and Finnish.

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